Uncertain Volatility Models

Theory and Application

Robert Buff (Autor)

Buch | Softcover

XII, 244 Seiten

2002
Springer Berlin (Verlag)
978-3-540-42657-8 (ISBN)

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Many introductory books on mathematical finance also outline some com puter algorithms. My goal is to contribute a closer look at algorithmic issues that arise from complex forms of the underlying pricing models-issues many practitioners need to solve sooner or later in their careers. This book takes such a close look at uncertain volatility models, an exten sion of Black-Scholes theory.It discusses applications to exotic option portfo lios with barriers and early exercise features. It describes an object-oriented C++ solution, included in source code on the accompanying CD. Practitioners and students who need to build analytic software libraries may benefit from reading this book and studying the software. The book focuses on a family of mathematical models, while in the field one encounters greater variation in instrument properties. In both cases mathematical and financial knowledge must be complemented by good programming skills to produce the best system. Analytic software needs design-a central message of the later chapters of this book. This book has come out of my Ph.D. thesis. I am very grateful to my academic advisor, Marco Avellaneda of New York University, who taught me mathematical finance and uncertain volatility. Computational finance be came exciting for me because Marco encouraged an algorithmic approach to uncertain volatility. I thank Afshin Bayrooti, Vladimir Finkelstein, and Antonio Paras for giving valuable feedback. Antonio is the co-inventor of the original uncertain volatility model, A-UVM. Richard Holmes has found a crucial bug in an early implementation of the software.

1 Introduction.- I Computational Finance: Theory.- 2 Notation and Basic Definitions.- 3 Continuous Time Finance.- 4 Scenario-Based Evaluation and Uncertainty.- II Algorithms for Uncertain Volatility Models.- 5 A Lattice Framework.- 6 Algorithms for Vanilla Options.- 7 Algorithms for Barrier Options.- 8 Algorithms for American Options.- 9 Exotic Volatility Scenarios.- III Object-Oriented Implementation.- 10 The Architecture of Mtg.- 11 The Class Hierarchy of MtgLib-External.- 12 The Class Hierarchy of MtgLib-Internal.- 13 Extensions for Monte-Carlo Pricing and Calibration.- A The Network Application MtgClt/MtgSvr.- B The Scripting Language MtgScript.- C Mathematica Extensions.- References.

From the reviews:

MATHEMATICAL REVIEWS

"The book bridges theory and real-world problems in a clear and pragmatic fashion. It can be useful both for academics and professionals in the financial community."

"This book, which comes out of the author's Ph.D. thesis, introduces uncertain volatility models. ... The formal results are illustrated by many empirical examples. ... The book bridges theory and real-world problems in a clear and pragmatic fashion. It can be useful both for academics and for professionals in the financial community." (Damir Filipovic, Mathematical Reviews, 2003 i)

"The book is devoted to the study of uncertain volatility models that evaluate option portfolios ... . The author travels in this book the entire road from innovative mathematical finance to a working software system ... . Practitioners and students who need to build analytic software libraries may benefit from reading this book ... . This book is also for graduate students and researchers who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options." (Anatoliy Swishchuk, Zentralblatt MATH, Vol. 1004 (4), 2003)

Erscheint lt. Verlag	10.4.2002
Reihe/Serie	Springer Finance
Reihe/Serie	Springer Finance Lecture Notes
Zusatzinfo	XII, 244 p. With online files/update.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	409 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Wirtschaft ► Allgemeines / Lexika
	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	algorithms • arbitrage pricing theory • Computational Finance • Mathematica • mathematical finance • Quantitative Finance • Uncertain volatility models • Volatilität
ISBN-10	3-540-42657-4 / 3540426574
ISBN-13	978-3-540-42657-8 / 9783540426578
Zustand	Neuware